In connection with the standardization of the European mobile phone system GSM plans have been made to include a facsimile service in the system with equipment configuration as shown in FIG. 1. The present facsimile terminals employ a modem interface and a 2-wire connection (modem connection), for example, via a telephone network. Thus, all signalling between fax terminals has taken place over a modem connection. In a digital cellular radio network at least one of the fax terminals would be disposed in connection with a mobile radio unit, whereby the fax connection must be established through a radio link between the mobile radio unit and the fixed network. In the GSM cellular radio system, this has been planned to be embodied in accordance with FIG. 1: a fax terminal 1 is connected in a normal manner over a 2-wire modem connection to a specific fax adaptor 2, by means of which the signals of the 2-wire connection are adapted to a specific data connection established over the radio link between the mobile radio unit MS and the base station system BSS to a mobile exchange MSC and further to a network terminating unit IWF comprising a second fax adaptor 5. The second fax adaptor 5 adapts the above-mentioned data connection to a conventional 2-wire modem connection, for example, through a public switched telephone network PSTN to another fax terminal. The implementation of a fax connection over a radio path involves, however, different kinds of problems, wherefore the standardization of the facsimile service according to FIG. 1 is still unaccomplished, and the facsimile service will not be available for the GSM users for some time.